1. Find the general solution to the following ODE:
y′′′+ 4y′= sec(2x)
2. Find the solution to the following IVP:
2y′′+ 2y′−2y= 6x2−4x−1
y(0) = −32
y′(0) = 5
3. Verify that y1=x1/2ln(x) is a solution
to
4x2y′′+y= 0,
and use reduction of order to find a second solution
y2.
4.
Find the general solutions to the following ODEs:
a) y′′′−y′= 0.
b) y′′+ 2y′+y= 0.
c) y′′−4y′+ 13y= 0.
Find the general solution to the differential equation below.
y′′ − 6y′ + 9y = 24t−5e3
Calculate the inverse Laplace transform of ((3s-2)
e^(-5s))/(s^2+4s+53)
Calculate the Laplace transform of y = cosh(at) using the
integral definition of the Laplace transform. Be sure to note any
restrictionson the domain of s. Recall that cosh(t)
=(e^t+e^(-t))/2
Second order Differential equation:
Find the general solution to [ y'' + 6y' +8y = 3e^(-2x) + 2x ]
using annihilators method and undetermined coeficients.